Stanford P. Yukon

Design of waveguides with prescribed propagation constants

Inverse scattering theory is applied to the design of optical waveguides possessing refractive-index profiles that support modes with prescribed propagation constants β. When gradient terms in the refractive index are neglected, we obtain explicit expressions for the refractive index of planar guides for which all β’s may be prescribed and of circularly symmetric guides, in which all β’s corresponding to a single fixed azimuthal mode number may be prescribed. When gradient terms are retained for planar guides it is only possible to prescribe the β’s for either TE or TM modes separately. For circular guides, when the gradient terms are retained, we have been able to obtain solutions to the inverse problem for the refractive-index profile for azimuthal mode number j = 1; again, one can only solve for either TE or TM modes separately. We demonstrate that the refractive index we have obtained for planar guides can be decomposed into solitons, and the known properties of solitons can be utilized to construct indices with specific characteristics. Finally, we apply the theory to the construction of profiles that enable “perfect” transmission of spatial images.

Residual lattice absorption in semiconducting crystals: frequency and temperature dependence.

Experimental and theoretical investigations of multiphonon absorption in semiconducting solids are conducted. We find that structure persists at lower absorption levels (~10(-2) cm(-1)) and at high temperatures (up to ~550 K) in these materials, in agreement with theoretical predictions. The theoretical analysis indicates that the observed rate of decrease of the absorption with increasing frequency is consistent with available models for the interionic potential and electric moments in these materials. Moreover, the structure in the spectrum is found to be almost exclusively a result of density of states effects, as opposed to k-selection rules.

Analog image transmission in optical waveguides

We have constructed a refractive index profile confined to a single waveguiding region, which permits analog transmission of one-dimensional spatial images along single optical waveguides.

Single-particle model for the frequency dependence of weak infrared absorption in crystals and molecules at T = 0 K

Abstract We obtain a simple expression for the infrared absorption coefficient α within the single-particle model at zero temperature. For potentials admitting harmonic approximation, α is found to decrease nearly exponentially with increasing frequency for small anharmonicity, with departures for larger anharmonicity. Potentials which do not admit harmonic approximation display a frequency dependence of the power-law variety. The present results in the quantum limit are similar to those obtained in the classical limit by Mills and Maradudin.

Residual lattice absorption in gallium arsenide

Abstract The residual lattice absorption of GaAs in the three and four phonon regime is measured over a range of temperatures. The spectra reveal persistent structural features which are interpreted theoretically in terms of phonon density of states effects.

Solitons in the Theory of Guided Lightwaves

It is well-known that wavepackets launched in a nonlinear medium will, in general, become broadened and distorted as a result of the nonlinearity.1,2 Nevertheless, in certain circumstances it is possible to obtain stable propagating solutions to nonlinear equations (referred to as “solitons”). In general, analytic solutions of this type are known to exist only for a few selected equations with a single spatial degree of freedom. Solitons retain their identity in much the same way as the normal modes of a linear system; they even emerge unscathed after “colliding” with each other. The mathematical nature of the equations involved and their associated solitons is well-exemplified by the two cases of interest in the present paper, namely, the nonlinear Schroedinger and Korteweg de Vries equations. Their principal characteristics are summarized briefly in the Appendix.

Theory of Multiphonon Absorption in Semiconducting Crystals

A correlation function approach is employed to calculate the multiphonon absorption in semiconducting crystals due to higher order electric moments, in the presence of anharmonicity. We find an exponential-like behavior for ω/ωo>>1, with broader absorption for increasing anharmonicity. Results of numerical computations within a simplified singleparticle model are presented for representative crystals.